Exactly solvable flow stability problems

Abstract

The method of separation of variables is applied to the problem of determining exactly solvable models of hydrodynamic stability. From a mathematical point of view, the problem of determining the stability of a flow is the solving of a system of equations derived from Navier-Stokes equations by linearization along the main flows and finding a set of all possible solutions that allow splitting of perturbations into normal modes. The case of cylindrical coordinates is completely considered.